JOSEPHSON-JUNCTION ARRAYS WITH LONG-RANGE INTERACTIONS

We calculate the current-voltage (IV) characteristics of a Josephson-j unction array with long-range interactions. The array consists of two sets of equally spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wir es cross. We treat each such junction as an overdamped resistively shu nted junction, and each wire segment between two junctions as a simila r resistively shunted junction with a much higher critical current. Th e IV characteristics are obtained by solving the coupled Josephson equ ations numerically. We find that, for a sufficiently large number of w ires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculate d IV characteristics also show a striking hysteresis, even though each of the individual junctions is non-hysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower v oltage branches, and is also in excellent agreement with experiment.